Given that the opposite sides of a parallelogram are congruent, a diagonal
of the parallelogram forms two congruent triangles.
The correct options to complete the proof are;
- Opposite sides of a parallelogram; ABCD is a parallelogram
- Reflexive property of congruency
Reasons:
The completed two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. ABCD is a parallelogram [tex]{}[/tex] 1. Given
2. [tex]\overline{AB}[/tex] ≅ [tex]\overline{DC}[/tex] and [tex]\overline{BC}[/tex] ≅ [tex]\overline{DA}[/tex] [tex]{}[/tex] 2. Opposite sides of a parallelogram
3. [tex]\overline{AC}[/tex] ≅ [tex]\overline{CA}[/tex] [tex]{}[/tex] 3. Reflexive property of congruency
4. ΔABC ≅ ΔCDA [tex]{}[/tex] 4. SSS
The correct options are therefore;
Opposite sides of a parallelogram; ABCD is a parallelogram
Reflexive property of congruency
SSS;
Reason 2. Opposite sides of a parallelogram, which is based on the
properties of a parallelogram and that ABCD is a parallelogram.
Reason 3. The reflexive property of congruency, states that a side is
congruent to itself.
Reason 4. SSS is an acronym for Side-Side-Side, which is a congruency
postulate that states that if the three sides of one triangle are equal to the
three sides of another triangle, then the two triangles are congruent.
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